Use the image to answer the question.

Question

Two parabolas and two inverted parabolas, all with arrows on both ends, are drawn on a coordinate plane with the x-axis from negative 6 to 6 and the y-axis from negative 6 to 6, both in increments of 1.

Given the graph of f(x)=(x+3)2
, which of the options is the graph of y=−f(x)
?

(1 point)
The graph of y=−f(x)
is option
.
Remaining Attempts : 3
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Answer 1

To find the graph of \( y = -f(x) \) given \( f(x) = (x+3)^2 \), we can follow these steps:

1. Understand the original function: The function \( f(x) = (x + 3)^2 \) is a standard parabola that opens upwards, with its vertex at the point (-3, 0).

2. Transform the function: The negative in front (\( y = -f(x) \)) indicates a reflection across the x-axis. This means every point on the graph of \( f(x) \) will flip to a corresponding point below the x-axis.

3. Determine the new vertex: Since the original vertex of \( f(x) \) is at (-3, 0), the vertex of \( y = -f(x) \) will be at (-3, 0), but it will open downwards.

4. Sketch or identify the characteristics of the graph: The graph of \( y = -f(x) \) will be a parabola that opens downwards, and it will look like a standard downward opening parabola with the same vertex at (-3, 0).

Look for the option that matches these characteristics—a downward-opening parabola that has its vertex at (-3, 0).

Without the actual image or specific options presented, you would identify which option corresponds to a downward-opening parabola centered at (-3, 0). Choose that option accordingly.